Journal of Function Spaces
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The latest articles from Hindawi Publishing Corporation
© 2015 , Hindawi Publishing Corporation . All rights reserved.

On Noncompact Fractional Order Differential Inclusions with Generalized Boundary Condition and Impulses in a Banach Space
Mon, 30 Mar 2015 13:52:16 +0000
http://www.hindawi.com/journals/jfs/2015/651359/
We provide existence results for a fractional differential inclusion with nonlocal conditions and impulses in a reflexive Banach space. We apply a technique based on weak topology to avoid any kind of compactness assumption on the nonlinear term. As an example we consider a problem in population dynamic described by an integropartialdifferential inclusion.
Irene Benedetti, Valeri Obukhovskii, and Valentina Taddei
Copyright © 2015 Irene Benedetti et al. All rights reserved.

Variational Inequalities with Multivalued Lower Order Terms and Convex Functionals in OrliczSobolev Spaces
Wed, 25 Mar 2015 13:02:54 +0000
http://www.hindawi.com/journals/jfs/2015/321437/
We consider the existence of solutions of variational inequality form. Find , whose principal part is having a growth not necessarily of polynomial type, where is a secondorder elliptic operator of LerayLions type, is a multivalued lower order term, and is a convex functional. We use subsupersolution methods to study the existence and enclosure of solutions in OrliczSobolev spaces.
Ge Dong and Xiaochun Fang
Copyright © 2015 Ge Dong and Xiaochun Fang. All rights reserved.

ThreePoint Boundary Value Problems for Conformable Fractional Differential Equations
Wed, 18 Mar 2015 15:40:13 +0000
http://www.hindawi.com/journals/jfs/2015/706383/
We study a fractional differential equation using a recent novel concept of fractional derivative with initial and threepoint boundary conditions. We first obtain Green's function for the linear problem and then we study the nonlinear differential equation.
H. Batarfi, Jorge Losada, Juan J. Nieto, and W. Shammakh
Copyright © 2015 H. Batarfi et al. All rights reserved.

New SetValued Integral in a Banach Space
Mon, 16 Mar 2015 13:52:29 +0000
http://www.hindawi.com/journals/jfs/2015/260238/
We introduce and study a new setvalued integral of scalarvalued functions with respect to a setvalued measure in a Banach space. We investigate some properties and convergence theorems for this kind of integral.
CaiLi Zhou and FuGui Shi
Copyright © 2015 CaiLi Zhou and FuGui Shi. All rights reserved.

On the Null Space Property of Minimization for in Compressed Sensing
Mon, 16 Mar 2015 10:03:16 +0000
http://www.hindawi.com/journals/jfs/2015/579853/
The paper discusses the relationship between the null space property (NSP) and the minimization in compressed sensing.
Several versions of the null space property, that is, the stable NSP, the robust NSP, and the robust NSP
for based on the standard NSP, are proposed, and their equivalent forms are derived.
Consequently, reconstruction results for the minimization can be derived easily under the NSP condition and its equivalent form.
Finally, the NSP is extended to the synthesis modeling and the mixed minimization,
which deals with the dictionarybased sparse signals and the block sparse signals, respectively.
Yi Gao, Jigen Peng, Shigang Yue, and Yuan Zhao
Copyright © 2015 Yi Gao et al. All rights reserved.

A Subordination Principle on Wright Functions and Regularized Resolvent Families
Mon, 16 Mar 2015 06:53:25 +0000
http://www.hindawi.com/journals/jfs/2015/158145/
We obtain a vectorvalued subordination principle for regularized resolvent families which unified and improves various previous results in the literature. As a consequence, we establish new relations between solutions of different fractional Cauchy problems. To do that, we consider scaled Wright functions which are related to MittagLeffler functions, the fractional calculus, and stable Lévy processes. We study some interesting properties of these functions such as subordination (in the sense of Bochner), convolution properties, and their Laplace transforms. Finally we present some examples where we apply these results.
Luciano Abadias and Pedro J. Miana
Copyright © 2015 Luciano Abadias and Pedro J. Miana. All rights reserved.

Space of Periodic Limit Functions and Its Applications to an Abstract Cauchy Problem
Sun, 15 Mar 2015 07:05:47 +0000
http://www.hindawi.com/journals/jfs/2015/953540/
We introduce a new space consisting of what we call periodic limit functions. We investigate some properties of the new function space. In particular, we study inclusion relations among asymptotically periodic type function spaces. Finally, we apply the periodic limit functions to investigate the existence and uniqueness of asymptotically periodic mild solutions of an abstract Cauchy problem.
Rui Xie and Chuanyi Zhang
Copyright © 2015 Rui Xie and Chuanyi Zhang. All rights reserved.

Toeplitz Operators on the Weighted Bergman Space over the TwoDimensional Unit Ball
Wed, 11 Mar 2015 10:52:23 +0000
http://www.hindawi.com/journals/jfs/2015/306168/
We extend the known results on commutative Banach algebras generated by Toeplitz operators with radial quasihomogeneous symbols on the twodimensional unit ball. Spherical coordinates previously used hid a possibility to detect an essentially wider class of symbols that can generate commutative Banach Toeplitz operator algebras. We characterize these new algebras describing their properties and, under a certain extra condition, construct the corresponding Gelfand theory.
Alma García and Nikolai Vasilevski
Copyright © 2015 Alma García and Nikolai Vasilevski. All rights reserved.

A Reverse Theorem on the  Continuity of the Dual Map
Tue, 10 Mar 2015 09:12:39 +0000
http://www.hindawi.com/journals/jfs/2015/864173/
Given a Banach space , , and , we define the set of all for which there exist two sequences and such that converges to , has a subnet convergent to , and for all . We prove that if is separable and reflexive and enjoys the RadonRiesz property, then is contained in the boundary of relative to . We also show that if is infinite dimensional and separable, then there exists an equivalent norm on such that the interior of relative to is contained in .
Mienie de Kock and Francisco Javier GarcíaPacheco
Copyright © 2015 Mienie de Kock and Francisco Javier GarcíaPacheco. All rights reserved.

The Singular Points of Analytic Functions with Finite Order Defined by LaplaceStieltjes Transformations
Mon, 02 Mar 2015 06:54:36 +0000
http://www.hindawi.com/journals/jfs/2015/865069/
We study the singular points of analytic functions defined by LaplaceStieltjes transformations which converge on the right half plane, by introducing the concept of order functions. We also confirm the existence of the finite order Borel points of such functions and obtained the extension of the finite order Borel point of two analytic functions defined by two LaplaceStieltjes transformations convergent on the right half plane. The main results of this paper are improvement of some theorems given by Shang and Gao.
HongYan Xu and ZuXing Xuan
Copyright © 2015 HongYan Xu and ZuXing Xuan. All rights reserved.

Jordan Type Inequalities for Hyperbolic Functions and Their Applications
Sun, 01 Mar 2015 14:16:04 +0000
http://www.hindawi.com/journals/jfs/2015/370979/
We present the best possible parameters p, such that the double inequality holds for all . As applications, some new inequalities for certain special function and bivariate means are found.
ZhenHang Yang and YuMing Chu
Copyright © 2015 ZhenHang Yang and YuMing Chu. All rights reserved.

Existence and Asymptotic Behaviour of Solutions of Differential and Integral Equations in Some Function Spaces
Sun, 01 Mar 2015 10:25:40 +0000
http://www.hindawi.com/journals/jfs/2015/235043/
Józef Banaś, Mohamed Abdalla Darwish, Leszek Olszowy, and Kishin Sadarangani
Copyright © 2015 Józef Banaś et al. All rights reserved.

Some Basic Properties of Certain New Subclass of Meromorphic Functions
Sun, 01 Mar 2015 08:03:31 +0000
http://www.hindawi.com/journals/jfs/2015/196060/
We introduce and investigate a new subclass of meromorphic functions. Some interesting properties such as inclusion relationship, coefficient estimates, neighborhoods, and partial sums are proved. Connections of the results with known results are also considered.
Lei Shi and ZhiGang Wang
Copyright © 2015 Lei Shi and ZhiGang Wang. All rights reserved.

Fixed Points of Modified Contractive Mappings in Complete MetricLike Spaces
Sat, 28 Feb 2015 09:48:32 +0000
http://www.hindawi.com/journals/jfs/2015/270971/
We introduce the notion of modified contractive mappings in the setting of complete metriclike spaces and we investigate the existence and uniqueness of fixed point of such mappings. The presented results unify, extend, and improve several results in the related literature.
Hamed H. Alsulami, Erdal Karapınar, and Hossein Piri
Copyright © 2015 Hamed H. Alsulami et al. All rights reserved.

Coefficient Estimates for Two New Subclasses of Biunivalent Functions with respect to Symmetric Points
Wed, 25 Feb 2015 08:33:12 +0000
http://www.hindawi.com/journals/jfs/2015/145242/
We introduce two subclasses of biunivalent
functions and find estimates on the coefficients and for functions in these new subclasses. Also, consequences of the results are pointed out.
Şahsene Altınkaya and Sibel Yalçın
Copyright © 2015 Şahsene Altınkaya and Sibel Yalçın. All rights reserved.

Picard Sequence and Fixed Point Results on Metric Spaces
Wed, 25 Feb 2015 07:06:24 +0000
http://www.hindawi.com/journals/jfs/2015/189861/
We obtain some fixed point results for singlevalued and multivalued mappings in the setting of a metric space. These results are generalizations of the analogous ones recently proved by Khojasteh, Abbas, and Costache.
Marta Demma and Pasquale Vetro
Copyright © 2015 Marta Demma and Pasquale Vetro. All rights reserved.

A New Characterization of Uniformly Rotund Banach Space
Tue, 24 Feb 2015 14:19:03 +0000
http://www.hindawi.com/journals/jfs/2015/865305/
A new characterization of uniformly rotund Banach space with
is given. Moreover, a corresponding result in the
locally uniformly rotund Banach space with is
given.
Suyalatu Wulede, Tingting Li, and Xuan Qin
Copyright © 2015 Suyalatu Wulede et al. All rights reserved.

Continuous Dependence of the Solutions of Nonlinear Integral Quadratic Volterra Equation on the Parameter
Mon, 23 Feb 2015 08:07:24 +0000
http://www.hindawi.com/journals/jfs/2015/471235/
We prove results on the existence and continuous dependence of solutions of a nonlinear quadratic integral Volterra equation on a parameter. This dependence is investigated in terms of Hausdorff distance. The considerations are placed in the Banach space and the Fréchet space.
Szymon Dudek and Leszek Olszowy
Copyright © 2015 Szymon Dudek and Leszek Olszowy. All rights reserved.

Inequalities Characterizing LinearMultiplicative Functionals
Mon, 23 Feb 2015 07:47:02 +0000
http://www.hindawi.com/journals/jfs/2015/945758/
We prove, in an elementary way, that if
a nonconstant realvalued mapping defined on a real algebra with a
unit satisfies certain inequalities, then it is a linear and multiplicative
functional. Moreover, we determine all Jensen concave and
supermultiplicative operators , where and are compact Hausdorff spaces.
Włodzimierz Fechner
Copyright © 2015 Włodzimierz Fechner. All rights reserved.

The Generalized Green’s Function for Boundary Value Problem of Second Order Difference Equation
Mon, 23 Feb 2015 06:37:20 +0000
http://www.hindawi.com/journals/jfs/2015/201946/
Let and . In this paper, by building the generalized Green’s function for the problems, we study the solvability of the SL problem , , , and the periodic SL problem , , where the parameter is an eigenvalue of the linear problem , , or the problem , , and , is defined and real valued on , and in the periodic SL problem we have .
Xiaoling Han and Juanjuan Huang
Copyright © 2015 Xiaoling Han and Juanjuan Huang. All rights reserved.

Some Classes of Continuous Operators on Spaces of Bounded VectorValued Continuous Functions with the Strict Topology
Sun, 22 Feb 2015 14:39:14 +0000
http://www.hindawi.com/journals/jfs/2015/796753/
Let be a completely regular Hausdorff space and let and be Banach spaces. Let be the space of all valued bounded, continuous functions on , equipped with the strict topology . We study the relationship between important classes of continuous linear operators (strongly bounded, unconditionally converging, weakly completely continuous, completely continuous, weakly compact, nuclear, and strictly singular) and the corresponding operator measures given by Riesz representing theorems. Some applications concerning the coincidence among these classes of operators are derived.
Marian Nowak
Copyright © 2015 Marian Nowak. All rights reserved.

Some Results for Periodic Solutions of a Kind of Liénard Equation
Sun, 22 Feb 2015 06:58:53 +0000
http://www.hindawi.com/journals/jfs/2015/519747/
We investigate the following Liénardtype Laplacian equation with a deviating argument . Some new criteria for guaranteeing the existence and uniqueness of periodic solutions of this equation are given by using the ManásevichMawhin continuation theorem and some analysis techniques. Our results hold under weaker conditions than some known results from the literature and are more effective. In the last section, an illustrative example is provided to demonstrate the applications of the theoretical results.
Yong Wang and Xiangyi Yi
Copyright © 2015 Yong Wang and Xiangyi Yi. All rights reserved.

On Traces in Some Analytic Spaces in Bounded Strictly Pseudoconvex Domains
Thu, 19 Feb 2015 10:34:05 +0000
http://www.hindawi.com/journals/jfs/2015/265245/
New sharp estimates of traces of Bergman type spaces of analytic functions in bounded strictly pseudoconvex domains are obtained. These are, as far as we know, the first results of this type which are valid for any bounded strictly pseudoconvex domains with smooth boundary.
Romi F. Shamoyan and Olivera R. Mihić
Copyright © 2015 Romi F. Shamoyan and Olivera R. Mihić. All rights reserved.

A General Uniqueness Theorem concerning the Stability of Additive and Quadratic Functional Equations
Tue, 17 Feb 2015 08:22:06 +0000
http://www.hindawi.com/journals/jfs/2015/643969/
We prove a general uniqueness theorem that can be easily applied to the (generalized) HyersUlam stability of the Cauchy additive functional equation, the quadratic functional equation, and the quadraticadditive type functional
equations. This uniqueness theorem can replace the repeated proofs for uniqueness of the relevant solutions of given equations while
we investigate the stability of functional equations.
YangHi Lee and SoonMo Jung
Copyright © 2015 YangHi Lee and SoonMo Jung. All rights reserved.

Volterra Type Integral Operators and Composition Operators on Model Spaces
Thu, 12 Feb 2015 13:08:30 +0000
http://www.hindawi.com/journals/jfs/2015/467802/
We study some mapping properties of Volterra type integral operators and composition operators on model spaces. We also discuss and give out a couple of interesting open problems in model spaces where any possible solution of the problems can be used to study a number of other operator theoretic related problems in the spaces.
Tesfa Mengestie
Copyright © 2015 Tesfa Mengestie. All rights reserved.

Ulam Problem for the Cosine Addition Formula in Sato Hyperfunctions
Thu, 12 Feb 2015 09:49:38 +0000
http://www.hindawi.com/journals/jfs/2015/615167/
We prove the Ulam problem for the cosine addition formula in the spaces of Schwartz distributions and Sato hyperfunctions with respect to bounded distributions and bounded hyperfunctions.
Jaeyoung Chung and SoonYeong Chung
Copyright © 2015 Jaeyoung Chung and SoonYeong Chung. All rights reserved.

Large Function Algebras with Certain Topological Properties
Tue, 10 Feb 2015 12:55:42 +0000
http://www.hindawi.com/journals/jfs/2015/761924/
Let be a family of continuous functions defined on a compact interval. We give a sufficient condition so that contains a dense generated free algebra; in other words, is densely strongly algebrable. As an application we obtain dense strong algebrability of families of nowhere Hölder functions, BrucknerGarg functions, functions with a dense set of local maxima and local minima, and nowhere monotonous functions differentiable at all but finitely many points. We also study the problem of the existence of large closed algebras within where or . We prove that the set of perfectly everywhere surjective functions together with the zero function contains a generated algebra closed in the topology of uniform convergence while it does not contain a nontrivial algebra closed in the pointwise convergence topology. We prove that an infinitely generated algebra which is closed in the pointwise convergence topology needs to contain two valued functions and infinitely valued functions. We give an example of such an algebra; namely, it was shown that there is a subalgebra of with generators which is closed in the pointwise topology and, for any function in this algebra, there is an open set such that is a Bernstein set.
Artur Bartoszewicz and Szymon Głąb
Copyright © 2015 Artur Bartoszewicz and Szymon Głąb. All rights reserved.

Representation of Group Isomorphisms: The Compact Case
Tue, 03 Feb 2015 08:54:51 +0000
http://www.hindawi.com/journals/jfs/2015/879414/
Let be a discrete group and let and be two subgroups of valued continuous functions defined on two 0dimensional compact spaces and
. A group isomorphism defined between and is called separating when,
for each pair of maps satisfying that , it holds that
. We prove that under some mild conditions every biseparating isomorphism can be represented by means of a continuous function as a weighted composition operator. As a consequence we establish
the equivalence of two subgroups of continuous functions if there is a biseparating
isomorphism defined between them.
Marita Ferrer, Margarita Gary, and Salvador Hernández
Copyright © 2015 Marita Ferrer et al. All rights reserved.

KorovkinType Theorems for Modular Statistical Convergence
Sat, 31 Jan 2015 13:22:48 +0000
http://www.hindawi.com/journals/jfs/2015/160401/
We deal with a new type of statistical convergence for double sequences, called statistical convergence, and we prove a Korovkintype approximation theorem with respect to this type of convergence in modular spaces. Finally, we give some application to momenttype operators in Orlicz spaces.
Carlo Bardaro, Antonio Boccuto, Kamil Demirci, Ilaria Mantellini, and Sevda Orhan
Copyright © 2015 Carlo Bardaro et al. All rights reserved.

Tricorns and Multicorns of Iteration Scheme
Wed, 28 Jan 2015 12:03:57 +0000
http://www.hindawi.com/journals/jfs/2015/417167/
Complex graphics of dynamical system have striking features of fractals and become a wide area of research due to their beauty and complexity of their nature. The aim of this paper is to study dynamics of relative superior tricorns and multicorns using iteration schemes. Several examples are presented to explore the geometry of relative superior tricorns and multicorns for antipolynomial of complex polynomial for .
Shin Min Kang, Arif Rafiq, Abdul Latif, Abdul Aziz Shahid, and Young Chel Kwun
Copyright © 2015 Shin Min Kang et al. All rights reserved.